## Statistical algorithms for circuit synthesis under process variation and high defect density

##### Abstract

As the technology scales, there is a need to develop design and optimization algorithms under various scenarios of uncertainties. These uncertainties are introduced by process variation and impact both delay and leakage. For future technologies at the end of CMOS scaling, not only process variation but the device defect density is projected to be very high. Thus realizing error tolerant implementation of Boolean functions with minimal redundancy overhead remains a challenging task. The dissertation is concerned with the challenges of low-power and area digital circuit design under high parametric variability and high defect density. The technology mapping provides an ideal starting point for leakage reduction because of higher structural freedom in the choices of implementations. We first describe an algorithm for technology mapping for yield enhancement that explicitly takes parameter variability into account. We then show how leakage can be reduced by accounting for its dependence on the signal state, and develop a fast gain-based technology mapping algorithm. In some scenarios the state probabilities can not be precise point values but are modeled as an interval. We extended the notion of mean leakage to the worst case mean leakage which is defined as the sum of maximal mean leakage of circuit gates over the feasible probability realizations. The gain-based algorithm has been generalized to optimize this proxy leakage metric by casting the problem within the framework of robust dynamic programming. The testing is performed by selecting various instance probabilities for the primary inputs that are deviations from the point probabilities with respect to which a point probability based gain based mapper has been run. We obtain leakage improvement for certain test probabilities with the interval probability based over the point probability based mapper. Next, we present techniques based on coding theory for implementing Boolean functions in highly defective fabrics that allow us to tolerate errors to a certain degree. The novelty of this work is that the structure of Boolean functions is exploited to minimize the redundancy overhead. Finally we have proposed an efficient analysis approach for statistical timing, which can correctly propagate the slope in the path-based statistical timing analysis. The proposed algorithm can be scaled up to one million paths.